Deep learning-enabled inverse mapping of elastic modulus fields from transient wave responses in heterogeneous materials

Accurate identification of spatially varying material properties is essential for understanding and predicting the mechanical behavior of heterogeneous structures. In this study, an elastic wave based inverse framework is developed for reconstructing the elastic modulus distribution in two dimensional inhomogeneous plates. Transient wave propagation is modeled using continuum mechanics based finite element formulation of linear elastodynamics. Material heterogeneity is introduced through element wise randomization of the elastic modulus within a prescribed range, while density and Poisson's ratio are assumed to be constant. A set of boundary actuators simultaneously generates short-duration rectangular displacement pulses, and the resulting wave responses are recorded by multiple receivers positioned along the opposite boundary. The simulated waveforms serve as input features for a deep neural network designed to predict the underlying elastic modulus field. A multilayer perceptron architecture is employed to capture the nonlinear relationship between transient wave signals and spatial stiffness variations. To enhance training stability and generalization, input standardization and normalization computed using training data only strategies are adopted. The results demonstrate that the proposed model successfully reconstructs heterogeneous elastic modulus distributions from limited wave measurements. The study highlights the potential of deep learning for non-destructive inverse characterization of inhomogeneous materials.